Visualizing Black Hole Spacetime with the Photon Ring

General relativity predicts that images of a rotating black hole ought to display a thin "photon ring" produced by strongly lensed photons that skirt the horizon. The Black Hole Explorer (BHEX), an orbiting sub-millimeter radio telescope, will work in tandem with ground-based observatories to take the sharpest images in the history of astronomy. BHEX's unprecedented resolution will enable a measurement of the photon ring around two supermassive black holes and deliver a measurement of their mass and spin. To make these inferences, it is crucial to understand the highly warped spacetime that bends photons into such strongly lensed trajectories. To that end, we present a series of visualizations of photon orbits in the Kerr geometry. In particular, we explore the seemingly chaotic behavior of the spacetime around the black hole, where two initially close photons can rapidly fly off along wildly divergent trajectories. In addition, we illustrate the "critical curve", the infinitely thin image of asymptotically trapped photons to which the photon ring asymptotes. Lastly, we render photon orbits within an embedding diagram that better conveys the curvature of spacetime. Each of these visualizations helps us develop our intuition for the nature of the photon ring and the Kerr geometry, enhancing our understanding and offering new insights in the study of black holes.